Hillary Clinton has admonished rival Donald Trump for claiming that she and Barack Obama were the founders of the Islamic State group, saying anyone who would "sink so low" should never be president.

Key points:

Analysts clarify that IS was founded years before Obama and Clinton

Trump doubles down, restating that it is the truth

US teen who scaled Trump Tower is charged

"No, Barack Obama is not the founder of ISIS," Mrs Clinton tweeted.

"Anyone willing to sink so low, so often should never be allowed to serve as our Commander-in-Chief."

Mr Trump again roiled the presidential campaign late on Wednesday, telling a rally in Florida that Mr Obama "is the founder of ISIS".

"And I would say, the co-founder would be crooked Hillary Clinton."

Republicans have long stated that the foreign policies of Mr Obama and his then-secretary of state Mrs Clinton share blame in helping create conditions that allowed IS militants to grow in Iraq and Syria.

But analysts have been quick to rectify Mr Trump's accusations, stating that the IS group's origins date back to 1999, and grew in strength as an Al Qaeda offshoot in 2006 following Republican president George W Bush's decision to invade Iraq in 2003.

Finally, in 2013 after a series of strategic victories, the Al Qaeda militant offshoot officially rebranded itself as the Islamic State group — known as IS or ISIS — months after Mrs Clinton left the State Department.

Republicans however have said Mr Obama was slow to recognise the threat when he said in 2014 that IS was a JV — junior varsity — team even though they gained ground in Syria and Iraq.

"It goes without saying that this is a false claim from a presidential candidate with an aversion to the truth and an unprecedented lack of knowledge," Mrs Clinton senior policy advisor Jake Sullivan said in a statement.

"This is another example of Donald Trump trash-talking the United States."

'Is there something wrong with saying that?': Trump

Mr Sullivan warned that Mr Trump was "echoing the talking points of [Russian President Vladimir)] Putin and our adversaries to attack American leaders and American interests, while failing to offer any serious plans to confront terrorism or make this country more secure."

Stephen Rogata, 19, from Great Falls in Virginia, was captured and dragged through a window on the 21st floor of the 68-story skyscraper around three hours after he embarked on his dare-devil stunt on Wednesday (local time).

New York police said on Thursday that he had been arrested and charged with reckless endangerment and criminal trespass.

Mr Trump, whom police said Mr Rogata wanted to meet, was out of town at the time on the campaign trail.